Most modem communications systems that operate near theoretical capacity limits employ equalization in the receiver to maximize the data rate. Multicarrier modulation systems such as discrete multitone (DMT) often use both time-domain equalization and frequency-domain equalization.
In typical DMT systems, data is segmented into blocks of N samples. At the transmitter, an inverse fast Fourier transform (IFFT) of the data is taken, and a cyclic prefix is appended to the beginning. For a length L cyclic prefix, this is done by appending the last L samples of the IFFT of the data to the beginning. At the receiver, the first L samples are skipped, and the remaining N samples are processed. If the channel length is shortened by the time-domain equalizer (TEQ) to L+1 samples or less, then the original data can be recovered by taking the fast Fourier transform (FFT) of the remaining N samples, and multiplying each resulting sample by the corresponding complex frequency-domain equalizer (FEQ) coefficient (effectively undoing the effects of the combined channel response at that frequency).
In order to achieve near capacity data rates the TEQ needs to compensate for intersymbol interference (ISI) due to the channel while at the same time appropriately filtering impairments such as echo, crosstalk, and radio frequency interference (RFI). These impairments tend to affect different parts of the channel. For typical frequency division duplex (FDD) deployments of asymmetrical digital subscriber lines (ADSL), a common DMT system, there is strong ISI (from bandsplit filters) and a large echo near the transition band. Higher up in frequency and farther away from the transition band the ISI and echo are less severe, but RFI is more likely to be present.
Using a single TEQ/FEQ to compensate for the impairments that affect different parts of the channel results in a performance tradeoff. The best TEQ in terms of data rate is not necessarily optimal for any particular part of the channel; however, it is also not bad for any particular part of the channel.